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Table of Contents
MOS
(maximally even scales indicated by *)generator = 1\41
[3] [4] [5] etc.
[40*] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
g=2 (hemimiracle)
[3] [4] [5] etc.
[20*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
[21*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
g=3 (octacot)
[3] [4] [5] etc.
[13] 3 3 3 3 3 3 3 3 3 3 3 3 5
[14*] 3 3 3 3 3 3 3 3 3 3 3 3 3 2
[27*] 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2
g=4 (miracle)
[3] [4] [5] etc.
[10*] 4 4 4 4 4 4 4 4 4 5
[11] 4 4 4 4 4 4 4 4 4 4 1
[21] 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1
[31*] 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1
g=5 (bohpier)
[8*] 5 5 5 5 5 5 5 6
[9] 5 5 5 5 5 5 5 5 1
[17] 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 1
[25] 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 1
[33*] 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1
note: the non-octave Bohlen-Pierce scale is simply 5 5 5 5 5 5 5 5 5 5 5 5 5, repeating at 3/1 (65\41)
g=6 (tetracot / bunya / monkey)
[7*] 6 6 6 6 6 6 5
[13] 1 5 1 5 1 5 1 5 1 5 1 5 5
[20] 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 4
[27] 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 3
[34*] 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2
g=7 (baldy)
[6*] 7 7 7 7 7 6
[11] 1 6 1 6 1 6 1 6 1 6 6
[17] 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 5
[23] 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 4
[29] [35*]
g=8 (rodan / guiron / slendric?)
[5*] 8 8 8 8 9
[6] 8 8 8 8 8 1
[11] 7 1 7 1 7 1 7 1 7 1 1
[16] 6 1 1 6 1 1 6 1 1 6 1 1 6 1 1 1
[21] 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 1
[26] [31] [36*]
g=9 (septimin)
[5] 9 9 9 9 5
[9*] 4 5 4 5 4 5 4 5 5
[14] 4 4 1 4 4 1 4 4 1 4 4 1 4 1
[23] 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 1
[32*] 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1
g=10 (quasitemp)
[4*] 10 10 10 11
[5] 10 10 10 10 1
[9] 9 1 9 1 9 1 9 1 1
[13] 8 1 1 8 1 1 8 1 1 8 1 1 1
[17] 7 1 1 1 7 1 1 1 7 1 1 1 7 1 1 1 1
[21] [25] [29] etc.
g=11 (superkleismic / orgone?)
[7] 3 8 3 8 3 8 8
[11] 3 3 5 3 3 5 3 3 5 3 5
[15*] 3 3 3 2 3 3 3 2 3 3 3 2 3 3 2
[26*] 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2
g=12 (hemififths / karadeniz / beatles?)
[7] 7 5 7 5 7 5 5
[10] 2 5 5 2 5 5 2 5 5 5
[17*] 2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3
[24*] 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1
g=13 (magic / witchcraft)
[7] 11 2 11 2 11 2 2
[10] 9 2 2 9 2 2 9 2 2 2
[13] 7 2 2 2 7 2 2 2 7 2 2 2 2
[16] 5 2 2 2 2 5 2 2 2 2 5 2 2 2 2 2
[19*] 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2
[22*] 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2
g=14 (hocus)
[3*] 14 14 13
[5] 1 13 1 13 13
[8] 1 1 12 1 1 12 1 12
[11] 1 1 1 11 1 1 1 11 1 1 11
[14] 1 1 1 1 10 1 1 1 1 10 1 1 1 10
[17] 1 1 1 1 1 9 1 1 1 1 1 9 1 1 1 1 9
[20] [23] [26] [29] etc.
g=15 (stacks?)
[5] 4 11 4 11 11
[8] 4 4 7 4 4 7 4 7
[11*] 4 4 4 3 4 4 4 3 4 4 3
[19] 1 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 3
[30*] 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2
g=16 (barbad)
[5] 7 9 7 9 9
[8] 7 7 2 7 7 2 7 2
[13] 5 2 5 2 2 5 2 5 2 2 5 2 2
[18*] 3 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2
[23*] 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2
g=17 (schismic / schismatic / helmholtz / garibaldi / cassandra)
[5] 10 7 10 7 7
[7] 3 7 7 3 7 7 7
[12*] 3 3 4 3 4 3 3 4 3 4 3 4
[17] 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 1
[29*] 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1
g=18 (trismegistus)
[5] 13 5 13 5 5
[7] 8 5 5 8 5 5 5
[9] 3 5 5 5 3 5 5 5 5
[16*] 3 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2
[25*] 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 2
g=19 (kangaroo? / thuja?)
[5] 16 3 16 3 3
[7] 13 3 3 13 3 3 3
[9] 10 3 3 3 10 3 3 3 3
[11] 7 3 3 3 3 7 3 3 3 3 3
[13*] 4 3 3 3 3 3 4 3 3 3 3 3 3
[15] 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3
[28*] 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2
g=20 (pluto)
[5] 19 1 19 1 1
[7] 18 1 1 18 1 1 1
[9] 17 1 1 1 17 1 1 1 1
[11] [13] [15] [17] etc.
g=21 <--> g=20
g=22 <--> g=19
etc.
Non-MOS
Harmonic series approximations
[5] 11 9 8 7 6 harmonic series 5:6:7:8:9:10[6] 9 8 7 6 6 5 harmonic series 6::12
[7] 8 7 6 6 5 5 4 harmonic series 7::14
[8] 7 6 6 5 5 4 4 4 harmonic series 8::16
[12] 5 4 4 4 4 3 3 3 3 3 2 3 harmonic series 12::24
(reverse these for subharmonic scales)
Others
from Scala:[7] 7 6 4 7 6 7 4 "just" major
[7] 7 4 6 7 4 7 6 "just" minor
[7] 7 4 6 7 4 6 7 natural minor
[7] 7 4 6 7 6 7 4 melodic minor
[7] 7 4 6 7 4 9 4 harmonic minor
[7] 7 6 4 7 4 9 4 harmonic major
[12] 4 3 4 2 4 3 4 4 2 4 3 4 "just" chromatic
...
Partial scales
Tetrachords
(from Scala)1 1 15 (0-1-2-17) Wilson
1 2 14 (0-1-3-17) Wilson
1 6 10 (0-1-7-17) Wilson
1 7 9 (0-1-8-17) Barbour Chromatic
2 2 13 (0-2-4-17) Ptolemy
2 5 10 (0-2-7-17) Archytas' Chromatic
2 7 8 (0-2-9-17) Septimal Kürdi
2 8 7 (0-2-10-17) Archytas' Diatonic, Ptolemy's Diatonon Toniaion
3 4 10 (0-3-7-17) Pythagorean Chromatic, Gaudentius
3 4 10 (0-3-7-17) Boethius Chromatic
3 4 10 (0-3-7-17) Perrett Chromatic
3 5 9 (0-3-8-17) Ptolemy
3 5 9 (0-3-8-17) Hipkins
3 6 8 (0-3-9-17) Ptolemy's Diatonon Malakon, Soft Diatonic
3 7 7 (0-3-10-17) Kürdi
3 7 7 (0-3-10-17) Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion
3 11 3 (0-3-14-17) Xenakis
4 4 9 (0-4-8-17) Avicenna
4 5 8 (0-4-9-17) Avicenna
4 6 10 (0-4-10-20) Araban
4 7 6 (0-4-11-17) Iraq, Segâh
4 9 4 (0-4-13-17) Sedaraban, Hicaz
4 9 4 (0-4-13-17) Palmer
4 10 3 (0-4-14-17) Evicârâ
5 5 7 (0-5-10-17) Ushshaq
5 5 7 (0-5-10-17) Young exquisite 3/4 tone Hellenic lyre
5 7 5 (0-5-12-17) Dudon Mohajira
5 7 5 (0-5-12-17) Mojahira, Iraq
7 2 7 (0-7-9-16) Nahawand
7 3 7 (0-7-10-17) Buselik
7 3 7 (0-7-10-17) Busalik, Nihâvend
7 4 6 (0-7-11-17) Müstear
7 4 9 (0-7-11-20) Neveser
7 5 5 (0-7-12-17) Rast
7 5 5 (0-7-12-17) Rast, Nagdi, Neutral Diatonic, Islamic Diatonic
7 5 5 (0-7-12-17) Modern Rast, Avicenna
7 6 4 (0-7-13-17) Turkish Rast
7 7 3 (0-7-14-17) Mahur
7 7 3 (0-7-14-17) Çargâh
8 7 2 (0-8-15-17) Septimal 'Ajam
Pentachords
(from Scala)3 7 7 7 (0-3-10-17-24) Kürdi
4 4 9 7 (0-4-8-17-24) Iranian
4 6 4 7 (0-4-10-14-21) Hicaz
4 7 6 7 (0-4-11-17-24) Segâh
5 5 7 7 (0-5-10-17-24) Huseyni
7 2 7 8 (0-7-9-16-24) Busalik
7 3 7 7 (0-7-10-17-24) Buselik
7 3 7 7 (0-7-10-17-24) Busalik
7 4 6 7 (0-7-11-17-24) Müstear
7 4 9 4 (0-7-11-20-24) Nikriz
7 5 5 7 (0-7-12-17-24) Rast
7 6 4 7 (0-7-13-17-24) Turkish Rast
7 7 3 7 (0-7-14-17-24) Çargâh
7 7 6 4 (0-7-14-20-24) Pencgâh